STORM: A General Model to Determine the Number and
Adaptive Changes of Epithelial Stem Cells in Teleost,
Murine and Human Intestinal Tracts
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Citation
Wang Z, Matsudaira P, Gong Z (2010) STORM: A General
Model to Determine the Number and Adaptive Changes of
Epithelial Stem Cells in Teleost, Murine and Human Intestinal
Tracts. PLoS ONE 5(11): e14063.
doi:10.1371/journal.pone.0014063
As Published
http://dx.doi.org/10.1371/journal.pone.0014063
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Public Library of Science
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Final published version
Accessed
Wed May 25 18:22:52 EDT 2016
Citable Link
http://hdl.handle.net/1721.1/64474
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STORM: A General Model to Determine the Number and
Adaptive Changes of Epithelial Stem Cells in Teleost,
Murine and Human Intestinal Tracts
Zhengyuan Wang1,2,3*, Paul Matsudaira1,2,3, Zhiyuan Gong1,2
1 Computation and Systems Biology, Singapore-MIT Alliance, Singapore, Singapore, 2 Department of Biological Sciences, National University of Singapore, Singapore,
Singapore, 3 Center for BioImaging Sciences, National University of Singapore, Singapore, Singapore
Abstract
Intestinal stem cells play a pivotal role in the epithelial tissue renewal, homeostasis and cancer development. The lack of a
general marker for intestinal stem cells across species has hampered analysis of stem cell number in different species and
their adaptive changes upon intestinal lesions or during development of cancer. Here a two-dimensional model, named
STORM, has been developed to address this issue. By optimizing epithelium renewal dynamics, the model examines the
epithelial stem cell number by taking experimental input information regarding epithelium proliferation and differentiation.
As the results suggest, there are 2.0–4.1 epithelial stem cells on each pocket section of zebrafish intestine, 2.0–4.1 stem cells
on each crypt section of murine small intestine and 1.8–3.5 stem cells on each crypt section of human duodenum. The
model is able to provide quick results for stem cell number and its adaptive changes, which is not easy to measure through
experiments. Its general applicability to different species makes it a valuable tool for analysis of intestinal stem cells under
various pathological conditions.
Citation: Wang Z, Matsudaira P, Gong Z (2010) STORM: A General Model to Determine the Number and Adaptive Changes of Epithelial Stem Cells in Teleost,
Murine and Human Intestinal Tracts. PLoS ONE 5(11): e14063. doi:10.1371/journal.pone.0014063
Editor: Stefan Wölfl, Universität Heidelberg, Germany
Received May 26, 2010; Accepted October 29, 2010; Published November 19, 2010
Copyright: ß 2010 Wang et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This work is supported by Singapore-MIT Alliance and Department of Biological Sciences of National University of Singapore. The funders had no role in
study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: wzhengyuan@gmail.com
fluctuations in cell death would render the exponential growth of
cells irriversible [15]. Johnston et al utilized both an age-structured
model and a continuous model to study epithelium homeostasis
and found that mutations in either death, differentiation or
renewal of stem cells or transit amplifying cells will initiate
tumorigenesis in the colon [11]. None of the models in current
literature, however, was designed to address the number of
intestinal stem cells and their adaptive changes.
In this work, a two-dimensional model has been developed to
examine the number of intestinal stem cells present in each twodimensional section of mammalian intestinal crypt, or inter-villus
pocket region of teleost intestines, taking input information gained
from experimental measurements. This is taking advantage of the
important fact that the intestinal epithelium renewal along the
crypt-villus axis is essentially a two-dimensional process [16,17,18].
It has been our aim to devise a simple and novel model that requires
minimal experimental input to directly address the stem cell
number. It has been named STORM model (STem cell mediated
Optimal Renewal of epithelium Model). As an illustration, the
model is applied to zebrafish, murine and human intestines, though
it may also be applied to other animal models. As the results suggest,
the stem cell number is largely conserved across species despite
differences among these animal models. In the mean time, the
analogy of intestinal epithelium renewal paradigm from zebrafish to
mouse and human has rendered zebrafish as an alternative model
for study of intestinal stem cells [19,20,21,22].
Introduction
The intestinal epithelium represents the most rapidly renewing
tissue in mammals [1]. It has been estimated that billions of cells
are exfoliated and replaced in the human intestine on a daily basis
[2]. The stem cells play a pivotal role in this process [3] and their
deregulation will lead to development of cancer, which is
becoming a leading killer in modern society [4,5]. Analysis of
the changes in the intestinal stem cell number upon occurrence of
any intestinal lesions would thus serve an important role. Up to
date, a general tool is not available for people to analyze the stem
cell number and their adaptive changes under different physiological and pathological conditions. This work aims to develop
such a tool that facilitates the analysis of stem cells in the intestinal
tracts of different species.
Current literature contains multitude of reports studying the
epithelium turnover process [6,7,8,9,10,11,12] by using either a
grid model [13], lattice-free model [7] or discrete multicompartmental model [9]. Epithelium migration, cell insertion
or apoptosis has been studied in these reports. For example,
Gerike et al studied dynamics of epithelium proliferation and
differentiation, where all columnar cells may become clonogenic
stem cells depending on the level of a hypothetical growth factor
[6]. Michor et al used probablity-based linear models to study the
dynamic effects of gene mutations in tumorigenesis [14]. Then
d’Onofrio et al proposed a non-linear model and suggested that
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heterzygous at the Dbl-1 locus showed that crypts drift toward
monoclonality in the small intestine [17,24]. Similarly, expression
analysis of X-chromosome related gene G6PD showed monoclonality of the crypts of large intestine [24]. The mechanism behind
these observations was further studied and the concept of neutral
competition was clearly proposed recently [25,26]. For instance, in
ref. [26], transgenic mice Lgr5-EGFP-Ires-CreERT2/E-cadherinmCFP and R26R-Confetti multicolor Cre-reporter were utilized
for lineage tracing in the intestine. This novely invented multicolor
tracing technique proved that descendants of stem cells constantly
went through neutral competition that drived all crypts toward
monoclonality in a few months (75% crypts monoclonal in 2
months and 100% in 6 months). Ultimately, descendants of a
particular stem cell with the optimal renewal efficiency won out
while others disappeared. These results led us to employ an
optimization method (to be shown below) to find out the optimal
dynamics of crypts as selected by the natural process.
Results
Development of the model
The model was developed based on two assumptions: (1)
Epithelial tissue was renewed in a stem cell – transit amplification –
differentiation – apoptosis paradigm; (2) The epithelial renewal
dynamics naturally evolved to have optimal restitutive efficiency.
Take zebrafish as an example. Proliferation assay based on
incorporation of bromodeoxyuridine was carried out for zebrafish
intestine. Results showed that cell proliferation was restricted in
the lower part of villi (Figure 1A, left panel). As the cells migrated
upward, they differentiated along either an absorptive or a
secretory fate to perform specialized functions. Once they reached
the tips of villi, they went through cell apoptosis, as shown by the
apoptosis assay (Figure 1A, middle panel), and were then
exfoliated. Based on these results, four compartments might be
identified along the villus axis, as illustrated in Figure 1B (right
panel). In other animals including mouse and human, the
intestinal epithelium was organized and renewed in essentially
the same manner [23]. Thus, our model was built on the general
paradigm of stem cell – transit amplification – differentiation – apoptosis
for intestinal epithelium, which was applicable to both teleost and
mammalian intestinal tracts.
Evidence for natural optimization of epithelial renewal
dynamics comes from literature. Mutational analysis of mice
Workflow of the model
The overall workflow of the model is illustrated in Figure 2. Based
on the assumptions mentioned earlier and using measured populations
of transit amplifying (TA) cells and differentiated cells, the optimization
formulation will find out the stem cell number as well as the adaptive
changes. Species-dependent outcome of the model would require
species-specific input information about the two populations of cells.
Figure 1. The paradigm of epithelium renewal in the intestine. (A) Cell proliferation and apoptosis in the intestine of zebrafish. Left panel: Cell
proliferation assay with proliferating cells stained dark brown. Middle panel: Cell apoptosis assay with apoptotic cells stained green. Right panel:
Compartmentalization of epithelium into stem cells, transit amplifying cells, differentiated cells and apoptotic cells. (B) The intestinal epithelium is
divided into four components while constructing the model, based on the analogous paradigm of epithelium renewal across teleost, murine and
human species. Stem cells maintain their own population through self-renewal, and in the mean time, they produce progenies that will differentiate
later on. Transit amplifying cells are directly derived from stem cells and go through rapid expansion. Then they go for cell differentiation and finally
apoptosis. Denotation: x1 - population of stem cells; x2 - population of transit amplifying cells; x3 - population of differentiated cells. Note that all
populations are normalized against their homeostatic populations in the model.
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Figure 2. Schematic illustration of the STORM model. The model takes experimental measurement of transit amplifying and differentiated cell
populations as input information. By optimizing the turnover dynamics, it yields the number of stem cells required on each section of pocket or crypt
of the intestine. It also provides information on epithelium turnover changes, for example, extended turnover cycles due to a reduction in the transit
amplifying cells.
doi:10.1371/journal.pone.0014063.g002
where c0 , c1 , k1 and k2 denote the rates of cell flux for the
population of stem cells, transit amplifying cells and differentiated
cells, respectively. It is worth noting that here we define the transit
amplifying cells as fast dividing cells that are derived from the stem
cells and they are not committed to any lineage yet. Those lineagecommitted cells will become part of the differentiated cells.
A non-trivial steady state may occur only if c1 = c0. If c1.c0, the
model exhibits exponential growth (unbounded growth of stem
cells); whereas if c1,c0, the model exhibits exponential decay
(extinction of stem cells and finally, of everything). Thus the
stability of this system depends on whether the relation c1 = c0
holds and the system is structurally unstable. Biological disturbances may easily lead to unbounded growth of cells. In order for
the system to maintain tissue homeostasis in a robust manner, as is
observed in the real world, it is necessary to incorporate a feedback
mechanism into the model.
A starting model for epithelium homeostasis
The process of epithelium turnover in the intestine is sketched in
Fig. 1B. This model is composed of three components: the stem
cells, the transit amplifying cells and the differentiated epithelial
cells. The population of stem cells is maintained through selfrenewal and production of progenies. The population of transit
amplifying cells is maintained through supply from stem cells and
expense to cell commitment. The population of differentiated
epithelial cells is maintained through supply from transit
amplifying progenitors and expense to apoptosis. All the
populations are normalized against their homeostatic populations,
respectively. Here, the stem cells are defined to be actively
involved in TA cell production (instead of remaining quiescent for
long periods of time); the TA population is defined to be fast
dividing cells that are derived from the stem cells and that are not
committed to any lineage yet. Once committed to a particular
lineage, either absorptive or secretory, they will be defined as part
of the differentiated population.
Based on Fig. 1B, a simple mathematical model can be derived
assuming that fluxes of cells move only in a one-way manner.
Transit amplifying cells do not reversely dedifferentiate to stem
cells (which was suggested a possibility under some special
circumstances [23]). Using denotations shown in Fig. 1B, a simple
model reads as follows:
dx1
~c1 x1 {c0 x1
dt
In view of the tight regulation on stem cells by various signals
from both epithelial and mesenchymal cells [27], the marginally
stable equation (1) hardly captures the homeostatic feature of the
stem cells [28]. Equation (1) may be modified to become
structurally stable based on the assumption that stem cell
differentiation is related to the second order of stem cell
population. Thus equation (1) becomes:
ð1Þ
dx1
~c1 x1 {c0 x21
dt
dx2
~c0 x1 {k1 x2
dt
ð2Þ
dx3
~k1 x2 {k2 x3
dt
ð3Þ
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The feedback mechanism in epithelium homeostasis
ð4Þ
Now the stem cell population may be maintained in a more robust
way, but this model still yields limited information about dynamics
k5 {x3
of the epithelium turnover process. Then a nonlinear term
k4 zx3
is incorporated into equation (2) and (3), introducing a saturable
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state of the tissue. Equations (5) and (6) are of special interest as
they contain the information on dynamics of epithelium turnover.
By setting their gradients to zero, only one non-trivial steady state
was found, which is {x2 ~1:0,x3 ~1:0}, just as we expected. The
Jacobian matrix of for equation (5) and (6) is given as follows:
feedback to stem cell self-renewal and transit amplifying cell
division [29,30,31,32,33,34,35,36,37,38].
In the mean time, a factor a, denoting the ratio of transit
amplifying population over stem cell population, and a factor b,
denoting the ratio of differentiated population over transit
amplifying population, were incorporated into the model,
respectively. To reflect the amplifying nature of the transit
population, a factor c is incorporated. Accordingly, the two
modified equations of (2) and (3) now read as follows:
dx2 c0
k5 {x3
x2 {k1 x2
~ x1 z
dt
a
k4 zx3
ð5Þ
dx3 ck1
k5 {x3
~
x2 z
x3 {k2 x3
dt
b
k4 zx3
ð6Þ
2
{
At steady state of {x2 ~1:0,x3 ~1:0}, the Jacobian matrix
simplifies as:
2
c0
6{ a
J(x ~1:0,x ~1:0) ~6
4 cc0
2
3
ab
The two nonlinear terms have been introduced with biological
support and they signify an important difference between our
model and previous models.
For euqation (5), the nonlinear term represents a link between
the TA population and the differentiated population. The link has
been demonstrated in mice genetically deficient in Muc2 (C57BL/
6J6129/SvOla Muc22/2), a mucin gene expressed only in
differentiated cells of the intestine, where impaired cell differentiation via Muc2 led to spontaneous development of adenomas
along the entire gastrointestinal tract [39,40], a pathology where
excessive cells remained proliferative. Similarly, through manipulation of Notch signaling, excessive cell proliferation was
observed, accompanied by impaired cell differentiation in the
intestine [41]. Conversely, excessive production of differentiated
cells was observed, which was accompanied by a reduction in
proliferative cells in the intestine, through utilization of RosaNotch/Cre+ mice [42]. These examples illustrate the inherent link
between populations x2 and x3 and mathematically, which is
modelled by the nonlinear term in equation (5).
For equation (6), the nonlinear term represents a self-fine-tuning
mechanism of the differentiated population. Biologically, it has
been known that there is certain level of overlap between transit
amplifying (fast dividing) cells and lineage committed cells in the
intestine. By utilizing the Math1beta-gal/beta-gal null mice, Yang et al
showed that some cells kept on dividing even after lineage
commitment, producing an overlapped staining by Ki67 and lacZ
reporter of these cells (representing the differentiation marker
Math1) [43], illustrating that these cells formed part of the
regulatory mechanism responsible for lineage generation process
in a self-fine-tuning manner.
The modified model consists of equations (4), (5), (6). As all cell
populations are normalized against their homeostatic values, they
are to be 1.0 when the system achieves tissue homeostasis. Thus we
have:
c0 ~c1 ~ak1 ~abk2 =c
ð7Þ
k5 ~1:0
ð8Þ
3
1
7
1zk4
7
cc0
1 5
{
{
ab 1zk4
{
ð10Þ
Its eigenvalues are given in two parts. The first part is given by:
P1eig(J ) ~{
s(bzc)
1
{
2b
2(1zk4 )
ð11Þ
The second part is given by:
1
2b(1zk4 )
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
b
ðs(1zk4 )(bzc)zbÞ2 {4sbc(1zk4 )(1z zszsk4 )
c
P2eig(J ) ~+
ð12Þ
where s~c0 =a. So the two eigenvalues are given by P1+P2. The
two eigenvalues have negative real part and the system is locally
stable. Upon perturbations, they may re-establish homeostasis with
different dynamics, depending on the parametric values (ie. organdependent and species-dependent).
The STORM formulation to estimate the epithelial stem
cell number
Following our second assumption on optimal restitutive
efficiency, the number of intestinal stem cells contained on each
section of crypt or inter-villus pocket may be determined by
solving the formulation:
s(bzc)
1
z
{
2b
2(1zk4 )
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
b
ðs(1zk4 )(bzc)zbÞ2 {4sbc(1zk4 )(1z zszsk4 )
2b(1zk4 )
c
ð13Þ
b
2
ðs(1zk4 )(bzc)zbÞ {4sbc(1zk4 )(1z zszsk4 )§0;
s:t:
c
(s,k4 )~ arg min s,k4 jc0 ,b,c {
s§0;
for the homeostatic state. This information will be utilized in the
following sections.
k4 §0:
ð13Þ
This is a two-dimensional, multi-variate optimization problem
with nonlinear objective function and nonlinear constraints.
s~c0 =a where c0 is directly related to the in vivo division frequency
of the stem cells. a denotes the population ratio of transit
Dynamics of the intestinal epithelium turnover process
The steady state of the system is (1.0, 1.0, 1.0) – normalized
against respective cell populations. It represents the homeostatic
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x2 (1{x3 )
x2
{
7
(k4 zx3 )2 k4 zx3
7
7 ð9Þ
cc0 (1{x3 )x3 1{2x3 5
z
{
{
ab (k4 zx3 )2 k4 zx3
co
1{x3
6 { a z k4 zx3
6
J(x2 ,x3 ) ~6
4
cc0
ab
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STORM Model for ISCs
amplifying cells over stem cells. b denotes the ratio of
differentiated epithelium over transit amplifying progenitors. c is
directly related to the in vivo division frequency of the transit
amplifying cells. Given the species-specific value of a, c and b, we
are able to find out the stem cell number by solving the above
formulation.
Formulation (13) may be solved with these parameter values.
After obtaining the stem cell number, the population of transit
amplifying cells needs to be corrected in order to produce a
posteriori-corrected value of b. Then the model needs to be solved
again. This posteriori-correction process is repeated several times
until the solution finally converges and will no longer change. The
final solution is as follows:
General characteristics of the crypt-villus system
There are some general results from the model, which may
provide some general knowledge about the crypt-villus system.
First, as an adaptive adjustment to the villus size in different
species (varying value of b), the ratio of stem cell over transit
amplifying cell will slightly increase for bigger ratio of b
(Figure 3A). This ratio is kept below 0.63 for all b not exceeding
30. For even bigger values of b, the epithelium renewal process
may be excessively slowed down (Figure 3B), rendering a
practically non-viable crypt-villus system for the host organism.
Second, the renewal cycle of epithelium is correlated to the ratio of
differentiated population over transit amplifying population (b).
For bigger value of b, the system needs to support a larger villus
size and the epithelium will be renewed at a lower rate. Figure 3B
shows the quantitative relationship.
To tailor the model to be species-specific, information about the
populations of transit amplifying cells, differentiated cells and in
vivo dividing frequency of stem cells will be evaluated based on
experimental results. The in vivo division frequency of intestinal
stem cells is not well characterized in the current literature, but it
has been speculated to be once or twice every day [44,45,46]. For
the transit amplifying cells, the amplifying factor c assumes the
value of 2.0.
b~10:3; s~
c0
~0:508
a
ð14Þ
As the population of transit amplifying cells is known from
proliferation assays, the number of stem cells may be calculated
given the ratio between transit amplifying cells and stem cells. The
result is as follows
4:1; Vc0 ~1
stem cell#~
2:0; Vc0 ~2
ð15Þ
The actual number of stem cells is dependent on their in vivo
division frequency. If stem cells only divide once per day, there
should be 4.1 stem cells present in each inter-villus pocket; if stem
cells divide twice per day, there will only be 2.0 stem cells required
in each inter-villus pocket. The results are summarized in Table 1.
To examine the adaptive changes in the number of stem cells,
the epithelium homeostasis was reduced by 50%, simulating
occurrence of intestinal lesions causing damage to the differentiated epithelium. The system responds by initiating tissue
restitution process. In the beginning stage, the value of b starts
at 4.0, the epithelium renewal cycle is 36% faster than the normal
cycle and this will trigger an expansion in the stem cell pool and
there will be 3.9 to 7.7 stem cells per pocket region (Figure 4A).
The expansion of stem cell pool supports a transient expansion of
transit amplifying population up to 14.5% (equivalent to one to
two cells; Figure 5). As new epithelium are being generated, the
ratio of b gradually grows back to normal value; The transit
amplifying and stem cell population will also return to their
respective homeostatic states upon completion of epithelium
restitution.
Determination of the stem cell number in the inter-villus
pocket region of zebrafish (Danio rerio) intestine
Cell counting over 200 villi in zebrafish based on our own
specimens shows the population of proliferating cells (including transit
amplifying cells and stem cells) to be 12.563.2 cells (mean6std) and
the population of differentiated cells with 100624 cells (mean6std).
Representative histological sections are shown in Figure 1A. Based on
these data, b assumes the value of 8.0 for zebrafish.
Figure 3. General relationships between s, t and b. (A) In general, s is positively correlated with b. For teleosts where b is smaller, s is lower; For
humans where b is bigger, s is higher. (B) The epithelium renewal cycle is also correlated to the value of b. Bigger value of b means longer renewal
cycle. Cycles are normalized to be dimensionless. s: dividing frequency|stem population/transit amplifying population; t: intestinal epithelium
renewal cycle; b: ratio of differentiated epithelium population/transit amplifying population.
doi:10.1371/journal.pone.0014063.g003
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restitution following 50% reduction in differentiated epithelium
are shown in Figure 3B, where the epithelium renewed 35% faster
than normal and the pool of stem cells expanded from 4.1 to 8.1
per section of crypt (Figure 4B), accompanied by a transient
expansion of transit amplifying population up to 14.7% (equivalent to one to two cells; Figure 5C).
Table 1. Stem cell number in the small intestine of different
species as suggested by STORM model.
Species
Stem cell
Stem cell
Priori-beta Posteriori-beta 1 division/day 2 divisions/day
Zebrafish 8.0
10.3
4.1
2.0
Mice
10.7
16.3
4.1
2.0
Human
23.1
39.0
3.5
1.8
Determination of the stem cell number in each crypt of
human duodenum
Proceeding as in the section for zebrafish, we obtained that the
population of differentiated epithelial cells in the villus is 120633;
the population of total cells in a crypt is 92612; the prioripopulation of proliferating cells (including transit amplifying cells
and stem cells) is 8.862.1(compiled from refs. [50,51,52,53]). So b
assumes the value of 23.1 for human duodenum.
Solve formulation (13) in a posteriori-correction manner to
have:
doi:10.1371/journal.pone.0014063.t001
The general correlation between stem cell number and
epithelium turnover cycle in zebrafish is shown in Figure 4A.
Determination of the stem cell number in each crypt of
murine small intestine
Proceeding as in the section for zebrafish, we obtained that the
population of differentiated epithelial cells is 96618 in the small
intestine of mice; the crypt population is 3868; the prioripopulation of proliferating cells (including transit amplifying cells
and stem cells) is 11.562.5 (the numbers estimated based on
references [27,29,42,45,47,48,49]). So b assumes the value of 10.7
for mouse small intestine.
Solve formulation (13) in a priori-posteriori correction manner
to have:
c0
b~16:3; s~ ~0:548
a
b~39:0; s~
ð18Þ
Based on the population of transit amplifying cells, the number of
stem cells may be calculated as follows
3:5; Vc0 ~1
stem cell#~
1:8; Vc0 ~2
ð19Þ
If stem cells only divide once per day, there should be 3.5 stem
cells present in each crypt; if stem cells are allowed to divide twice
per day, there will only be 1.8 stem cells in each crypt. The results
are summarized in Table 1.
Similar perturbation was applied as before. Results are shown in
in Figure 3B, where the epithelium renewed 40% faster than
normal and the stem cells expanded from 4.3 to 8.6 per section of
crypt (Figure 4C), accompanied by a transient expansion of transit
amplifying population up to 11% (equivalent to one cell;
Figure 5C).
ð16Þ
Based on the population of transit amplifying cells, the number of
stem cells may be calculated as follows
4:1; Vc0 ~1
stem cell#~
2:0; Vc0 ~2
c0
~0:665
a
ð17Þ
If stem cells only divide once per day, there should be 4.1 stem
cells present in each crypt; if stem cells are allowed to divide twice
per day, there will only be 2.0 stem cells required in each crypt.
Results are summarized in Table 1.
Similar perturbation was conducted to examine the adaptive
changes in the number of stem cells in mice. Results of tissue
Comparison of the intestines of different species
To compare the epithelium renewal paradigm among three
different species, the ratios between stem cells, transit amplifying
cells and differentiated cells are plotted in Figure 5A&B. There is a
higher transit amplifying-to-stem cell ratio in teleost. It is the
Figure 4. Adaptive changes in the intestinal stem cell number. (A) Intestine of zebrafish. (B) Small intestine of mouse. (C) Duodenum of
human. Upper and lower limits of the division frequency of stem cells in vivo (once to twice per day) define a range of the number of stem cells
required to be present on each section of inter-villi pocket in zebrafish intestine. Reduction in cell proliferation would result in a bigger value of b and
thus a prolonged epithelium renewal cycle. That would be accompanied by less number of stem cells around. On the other hand, enhanced cell
proliferation would result in a smaller value of b and thus an accelerated epithelium renewal process, accompanied by an increase in stem cell
population. That would be the case where hyperplasia or adenoma starts to develop.
doi:10.1371/journal.pone.0014063.g004
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Figure 5. Comparison of epithelium renewal dynamics in different species. (A) The transit amplifying-to-stem cell ratio is the highest in
teleost but the lowest in human during normal homeostasis. (B) The differentiated-to-transit amplifying cell ratio is the lowest in teleost but the
highest in human during normal homeostasis. (C) As a strategy of efficient tissue restitution, there will be a transient expansion of the transit
amplifying population by 10–15% in these species. This value does not vary much as long as the lesion ranges below ,95% of the epithelium tissue.
(D) Recovery time varies in these species. In teleost, epithelium can be restituted in a shorter period of time, but this is achieved by allowing a bigger
transient expansion in the transit amplifying population. In human, it takes longer time to complete epithelium restitution, but this is achieved with a
tighter mediation over the expansion of the transit amplifying population. These data suggest that these species employ different strategies in
maintenance of homeostasis. Compared with intestines of other species, human intestine harbors minimum number of stem cells to support a larger
villus size and restitutes epithelium through tightly mediated proliferation to maintain genome integrity and minimize the possibility of carcinogenic
transformations.
doi:10.1371/journal.pone.0014063.g005
lowest in human accompanied by a higher differentiated-to-transit
amplifying cell ratio. This probably reflects two different strategies
in the epithelium renewal mechanism: Rapid repair and quick
restitution of epithelium take higher priority in the teleost system,
whereas relatively slower tissue repair and restitution are allowed
in human, with achievement of high fidelity in genomic
duplication and reduction in susceptibility of carcinogenic
transformations.
The process of tissue restitution takes relatively longer time in
human, but the transit amplifying population is better restrained
from excessive expansion compared with murine and teleost
models (Figure 5C&D). This is important as unrestrained
expansion of transit amplifying population will lead to development of cancer. As the model reveals, that may happen during
epithelium restitution in teleost and murine models, but it is less
likely in human intestine (Figure 6).
duodenal ulcer and 17.861.5 in duodenitis. Utilizing these data,
the model yields that: (1) For duodenal ulcer, s~0:419,
t=t0 ~0:54, stem cell = 8 on average (In normal human
duodenum, the stem cell number is 1.8–2.7, averaged 4.0 as
shown earlier). The chi-test for duodenal ulcer shows that it is
significantly different from the healthy duodenum (p,0.003). As
the output suggests, there is an increase in the stem cell
population and an accelerated epithelium renewal rate (about
two-fold faster compared with normal rate), implying duodenal
hyperplasia. (2) For duodenitis, s~0:444, t=t0 ~0:60, stem
cell = 7.5 on average. The chi-test for duodenitis shows that it is
significantly different from the healthy duodenum (p,0.02). As
the output suggests, there is an increase in the stem cell
population and an accelerated epithelium renewal rate (about
1.7-fold faster), implying duodenal hyperplasia. The actual
presence of hyperplasia is further evidenced by the histological
results of biopsies from the patients, in consistence with analysis
result of the current model.
Application of the model to help evaluate hyperplasia in
human duodenitis and ulcer
Previously, Bransom et al reported of mucosal cell proliferation
in the duodenum with duodenitis or ulcer in endoscopic biopsies
[51]. They intended to find out the presence of epithelium
hyperplasia. That may be achieved by quantitative analysis using
this model. Based on the histological results, the villi were
shortened by 30–50% in duodenal ulcer and duodenitis.
Epithelium proliferation, as indicated by the labeling index (the
ratio of labeled nuclei to total nuclei in the crypt) is 15.661.7 in
PLoS ONE | www.plosone.org
Discussion
A novel model for stem cell number in the intestine
In this work, we have devised a novel model that directly
addresses stem cell number in the intestine. Utilizing the
biological finding of the partial overlap between the transit
amplifying population and the differentiated population [1,43],
we introduced nonlinear terms accordingly to model the renewal
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November 2010 | Volume 5 | Issue 11 | e14063
STORM Model for ISCs
Figure 6. Changes in cell populations during epithelium restitution. The transit amplifying population will transiently expand during
epithelium restitution. In the case of extreme tissue lesion where more than 90% tissue is damaged, there will be an overwhelming response of the
crypt-villus system and the transit amplifying population will expand in an uncontrolled manner, producing intestinal hyperplasia or adenoma in the
teleost and murine intestines, though it seems less likely in human intestine. Denotation: . for zebrafish; for mouse; & for human.
doi:10.1371/journal.pone.0014063.g006
N
process in two-dimension. As the intestinal stem cells constantly
compete against each other for optimal renewal dynamics
[25,26], the optimization formulation was devised following this
philosophy. Solution to the optimal model then allowed us to
infer the stem cell number. Design of the model based on the
general stem cells – TA cells – differentiated cells – apoptosis paradigm
has made it possible for the model to be applied to intestines of
different species. To our best knowledge, this is the first model of
its kind ever reported so far.
Achieving optimal epithelium renewal rate is essential to
sustainable organ function
The renewal rate of the intestinal epithelium tissue becomes
critical in terms of maintenance of tissue integrity, organ function
and potential risk of carcinogenic transformation during the life
span of the host organism. A high turnover rate would allow quick
restitution of the lost tissue due to damage; but on the other hand,
high turnover rate would require the presence of more active stem
cells around and more frequent cell divisions, increasing the
susceptibility to genome duplication-induced mutations and the
risk of carcinogenic transformation of the intestinal tissue. These
two opposing requirements ultimately lead to optimization of the
epithelium turnover rate for a defined organism, allowing
maintenance of tissue integrity and organ function with minimal
stem cells and cell divisions required. This may be the driving force
behind the neutral competition dynamics, and this optimizing
procedure persists throughout the adulthood [25,26]. The
optimization model based on this principle has successfully yielded
estimates of the stem cell number contained on a section of crypt
or inter-villi pocket , and they largely agrees with previous
speculations [45,54].
Linear migration of epithelial cells simplifies threedimensional crypt-villus structures into a twodimensional model
Though the villi and crypts constitute a three-dimensional inner
surface of the intestine, the linear nature of epithelial cell migration
[16,17,18] nicely simplifies the tissue renewal process into a twodimensional model. Cell proliferation is restricted near the bottom
of crypts (in mammals) or in the inter-villus pocket region (in
cryptless zebrafish), whereas apoptosis is restricted at the tips of
villi. Epithelium is renewed through cell migration along the villus
axis. All cells except the Paneth cells are migrating upward,
including columnar cells, goblet cells and enteroendocrine cells in
the two-dimensional model.
Differences have been noticed between the two-dimensional
systems. In mouse, only a few number of cells are going through
apoptosis along each villus (about 7 apoptotic cells over 100 villi
[48]). While in contrast, the number of apoptotic cells is notably
larger in zebrafish, typically around 15–20 cells per section of
villus (Figure 1A). The difference in cell apoptosis agrees with
what the model suggests that tissue renewal process goes faster in
zebrafish than in mammals (Figure 3B) and in case of tissue
recovery, the system recovered more quickly in zebrafish
(Figure 5D).
PLoS ONE | www.plosone.org
STORM model has produced data in general agreement
with previous literature
In previous reports, Bjerknes et al [16] and Potten [23,54]
estimated that there were 4–6 stem cells in each crypt of mouse
intestine (in three dimension). The recent work by Barker et al
[55,56], through discovery of stem cell marker Lgr5, showed 6
identifiable stem cells in a section of crypt. Based on their
histological results [55,56], there were approximately 3.5 stem cells
per crypt per histological section. Thus in terms of twodimensional section, our model is able to produce data that
generally agree with previous experimental measurements.
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STORM Model for ISCs
As no stem cell marker has been established in zebrafish or
human, verification of the model results still awaits future work in
this field.
Histology
Intestines were isolated from euthanized adult zebrafish, washed
in ice-cold phosphate-buffered saline (PBS), fixed overnight in a
4% paraformaldehyde solution in PBS at room temperature. Fixed
tissue was dehydrated in ethanol with increasing gradients (75%,
90%, 95%, 100% twice), cleared in histoClearII twice and
embedded overnight in paraffin that was melted at 58uC. Samples
were then sectioned at 7 mM using a Reichert-Jung 2030 machine.
The number of stem cells appears to be conserved in
each pocket/crypt of teleost, murine and human
intestines
Despite differences in the intestinal epithelium from teleost to
murine, the stem cell number appears conserved within these
species. In general, it seems not necessary to maintain a large
number of stem cells around from day to day, due to their
immortality, sensitivity to DNA damage and carcinogenic
potential [57,58,59]. In presence of an amplifying mechanism,
tissue homeostasis and restitution may be achieved with efficiency
by the transit amplifying population without an emergency call on
the multipotent stem cells. The human intestine, however, appears
to be a more robust system with a more restricted transient
expansion in the TA population. This feature may help minimize
the potential risk of tumor develpment during the long life-span of
humans, compared with teleosts and mice.
Immunohistochemistry
25mM Bromodeoxyuridine (Sigma-aldrich, St Louis, United
States) was orally administered 50uL per fish 10 minutes before
they were euthanized. Immunohistochemistry was performed
according to the manufacturer’s protocol (cat# 2760, Chemicon
International, United States). Briefly, the slides were cleared in
histoClear, rehydrated and quenched in 3% hydrogen peroxide,
incubated in 0.2% trypsin solution for 10 minutes, denatured for
30 minutes. Slides were subjected to blocking solution for
10 minutes before incubation with detector antibody for 60 minutes at room temperature. Then streptavidin-horse radish
peroxidase conjugate was applied for 10 minutes and slides were
subjected to a mixture of diaminobenzidine and substrate reaction
buffer until color developed. The slides were covered by coverslips
and sealed by DePex mounting medium and later, images were
taken using a Zeiss Axiovert imaging system.
Immunofluorescent TUNEL assay was carried out according to
the manufacturer’s protocol (S7111, Chemicon International,
United States). Briefly, slides were dewaxed in histoClear,
rehydrated and incubated in proteinase K (20 mg/ml) for
15 minutes at room temperature. Equilibration buffer was applied
before incubation in terminal deoxyribonucleic transferase enzyme
in a humidified chamber at 37uC for 60 minutes. Then stop buffer
was applied before slides were incubated in anti-digoxigenin
conjugate solution in a humidified chamber for 30 minutes at
room temperature in dark. The slides were incubated in 0.5 mg/ml
propidium iodide for 10 minutes as a fluorescent counterstaining
of nuclei. Finally the slides were covered by coverslips, sealed by
DePex mounting medium and images were taken using a Zeiss
Axiovert imaging system.
A general model for analysis of stem cell number with
equal applicability to teleost, murine and human
intestinal tracts
For the first time, a general model is developed to analyze the
number of stem cells in the intestinal tracts of teleost, murine and
human with minimal requirement of input: mainly information on
cell proliferation and differentiation (Figure 2). The fact that the
intestinal epithelial cells are essentially renewed in a linear manner
[16,17,18] has allowed us to develop a two-dimensional model to
estiamte the number of stem cells on a section of crypt (or an intervilli pocket). In absence of a universal stem cell marker for all
species, this model provides a useful tool for us to examine the
adaptive changes in stem cell number and epithelium renewal
dynamics during physiological and pathological states of the
organ.
Methods
Acknowledgments
The work is approved by Institutional Animal Care and Use
Committee (IACUC), National University of Singapore with the
approval ID: 070/09.
The authors would like to thank Singapore-MIT Alliance and Department
of Biological Sciences of National University of Singapore for support of
this work.
Maintenance of zebrafish (Daino rerio)
Zebrafish were obtained from local aquarium supply and
maintained in a controlled environment according to standard
condition with a 14/10 hour light-dark cycle at 28uC [60].
Author Contributions
Conceived and designed the experiments: ZW PM ZG. Performed the
experiments: ZW. Analyzed the data: ZW ZG. Contributed reagents/
materials/analysis tools: ZG. Wrote the paper: ZW PM ZG.
References
8. Paulus U, Loeffler M, Zeidler J, Owen G, Potten C (1993) The differentiation
and lineage development of goblet cells in the murine small intestinal crypt:
experimental and modelling studies. J Cell Sci 106: 473–483.
9. Paulus U, Potten C, Loeffler M (1992) A model of the control of cellular
regeneration in the intestinal crypt after perturbation based solely on local stem
cell regulation. Cell Prolif 25: 559–578.
10. Tomlinson I, Bodmer W (1995) Failure of programmed cell death and
differentiation as causes of tumors: some simple mathematical models. Proc Natl
Acad Sci USA 92: 11130–11134.
11. Johnston M, Edwards C, Bodmer W, Maini P, Chapman J (2007) Mathematical
modeling of cell population dynamics in the colonic crypt and in colorectal
cancer. Proc Natl Acad Sci USA 104: 4008–4013.
12. Boman B, Fields J, Bonham-Carter O, Runquist O (2001) Computer modeling
implicates stem cell overproduction in colon cancer initiation. Cancer Res 61:
8408–8411.
1. Crosnier C, Stamataki D, Lewis J (2006) Organizing cell renewal in the intestine:
stem cells, signals and combinatorial control. Nature Rev Genetics 7: 349–359.
2. Potten C, Wilson J (2004) Apoptosis: The life and death of cells. New York:
Cambridge University Press. pp 136–183.
3. Potten CS (1984) Clonogenic, stem and carcinogen-target cells in small intestine.
Scand J Gastroenterol Suppl 104: 3–14.
4. Jemal A, Siegel R, Ward E, Hao Y, Xu J, et al. (2008) Cancer statistics, 2008.
CA Cancer J Clin 58: 71–96.
5. Jemal A, Siegel R, Ward E, Murray T, Xu J, et al. (2007) Cancer statistics, 2007.
CA Cancer J Clin 57: 43–66.
6. Gerike T, Paulus U, Potten C, Loeffler M (1998) A dynamic model of
proliferation and differentiation in the intestinal crypt based on a hypothetical
intraepithelial growth factor. Cell Prolif 31: 93–110.
7. Meineke F, Potten C, Loeffler M (2001) Cell migration and organization in the
intestinal crypt using a lattice-free model. Cell Prolif 34: 253–266.
PLoS ONE | www.plosone.org
9
November 2010 | Volume 5 | Issue 11 | e14063
STORM Model for ISCs
13. Loeffler M, Potten C, Paulus U, Glatzer J, Chwalinski S (1988) Intestinal crypt
proliferation. II. Computer modelling of mitotic index data provides further
evidence for lateral and vertical cell migration in the absence of mitotic activity.
Cell Tissue Kinet 21: 247–258.
14. Michor F, Iwasa Y, Lengauer C, Nowak MA (2005) Dynamics of colorectal
cancer. Semin Cancer Biol 15: 484–493.
15. d’Onofrio A, Tomlinson IP (2007) A nonlinear mathematical model of cell
turnover, differentiation and tumorigenesis in the intestinal crypt. J Theor Biol
244: 367–374.
16. Bjerknes M, Cheng H (1999) Clonal analysis of mouse intestinal epithelial
progenitors. Gastroenterology 116: 7–14.
17. Winton DJ, Blount MA, Ponder BA (1988) A clonal marker induced by
mutation in mouse intestinal epithelium. Nature 333: 463–466.
18. Winton DJ, Ponder BA (1990) Stem-cell organization in mouse small intestine.
Proc Biol Sci 241: 13–18.
19. Wallace K, Pack M (2003) Unique and conserved aspects of gut development in
zebrafish. Dev Biol 255: 12–29.
20. Wallace K, Akhter S, Smith E, Lorent K, Pack M (2005) Intestinal growth and
differentiation in zebrafish. Mech Dev 122: 157–173.
21. Ng N, Jong-Curtain T, Mawdsley D, Heath J (2005) Formation of the digestive
systen in zebrafish: III. Intestinal epithelium morphogenesis. Developmental
Biology 286: 114–135.
22. Crosnier C, Vargesson N, Gschmeissner S, Ariza-McNaughton L, Morrison A,
et al. (2004) Dolta-Notch signalling controls commitment to a secretory fate in
the zebrafish intestine. Development 132: 1093–1104.
23. Booth C, Potten C (2000) Gut instincts: thoughts on intestinal epithelial stem
cells. The Joutnal of Clinical Investigation 105: 1493–1499.
24. Griffiths DF, Davies SJ, Williams D, Williams GT, Williams ED (1988)
Demonstration of somatic mutation and colonic crypt clonality by X-linked
enzyme histochemistry. Nature 333: 461–463.
25. Lopez-Garcia C, Klein AM, Simons BD, Winton DJ (2010) Intestinal Stem Cell
Replacement Follows a Pattern of Neutral Drift. Science.
26. Snippert HJ, van der Flier LG, Sato T, van Es JH, van den Born M, et al. (2010)
Intestinal crypt homeostasis results from neutral competition between symmetrically dividing Lgr5 stem cells. Cell 143: 134–144.
27. Mills J, Gordon J (2001) The intestinal stem cell niche: There grows the
neighborhood. Proc Natl Acad Sci USA 98: 12334–12336.
28. Bach SP, Renehan AG, Potten CS (2000) Stem cells: the intestinal stem cell as a
paradigm. Carcinogenesis 21: 469–476.
29. Bjerknes M, Cheng H (2001) Modulation of specific intestinal epithelial
progenitors by enteric neurons. Proc Natl Acad Sci USA 98: 12497–12502.
30. Rubin D (2007) Intestinal morphogenesis. Curr Opin gastroenterol 23: 111–114.
31. He X, Zhang J, Li L (2005) Cellular and molecular regulation of hematopoietic
and intestinal stem cell behavior. Ann N Y Acad Sci 1049: 28–38.
32. Rijke RP, Hanson WR, Plaisier HM, Osborne JW (1976) The effect of ischemic
villus cell damage on crypt cell proliferation in the small intestine: evidence for a
feedback control mechanism. Gastroenterology 71: 786–792.
33. Galhaard H, Van Der Meer-Fieggen W, Giesen J (1972) Feedback control by
functioning villus cells on cell proliferation and maturation in intestinal
epithelium. Exp Cell Res 72: 197–207.
34. Powell D, Mifflin R, Valentich J, Crowe S, Saada J, et al. (1999) Myofibroblasts.
II. Intestinal subepithelial myofibroblasts. Am J Physiol 277: C183–201.
35. Li X, Madison B, Zacharias W, Kolterud A, States D, et al. (2007)
Deconvoluting the intestine: molecular evidence for a major role of the
mesenchyme in the modulation of signaling cross talk. Physiol Genomics 29:
290–301.
36. Ahuja V, Dieckqraefe B, Anant S (2006) Molecular biology of the small intestine.
Curr Opin Gastroenterol 22: 90–94.
37. Ishizuya-Oka A (2007) Regeneration of the amphibian intestinal epithelium
under the control of stem cell niche. Dev Growth Differ 49: 99–107.
PLoS ONE | www.plosone.org
38. Walters J (2004) Cell and molecular biology of the small intestine: new insights
into differentiation, growth and repair. Curr Opin Gastroenterol 20: 70– 76.
39. Velcich A, Yang W, Heyer J, Fragale A, Nicholas C, et al. (2002) Colorectal
cancer in mice genetically deficient in the mucin Muc2. Science 295:
1726–1729.
40. Yang K, Popova NV, Yang WC, Lozonschi I, Tadesse S, et al. (2008)
Interaction of Muc2 and Apc on Wnt signaling and in intestinal tumorigenesis:
potential role of chronic inflammation. Cancer Res 68: 7313–7322.
41. Fre S, Huyghe M, Mourikis P, Robine S, Louvard D, et al. (2005) Notch signals
control the fate of immature progenitor cells in the intestine. Nature 435:
964–968.
42. van Es JH, van Gijn ME, Riccio O, van den Born M, Vooijs M, et al. (2005)
Notch/gamma-secretase inhibition turns proliferative cells in intestinal crypts
and adenomas into goblet cells. Nature 435: 959–963.
43. Yang Q, Bermingham NA, Finegold MJ, Zoghbi HY (2001) Requirement of
Math1 for secretory cell lineage commitment in the mouse intestine. Science
294: 2155–2158.
44. Li Y, Roberts S, Paulus U, Loeffler M, Potten C (1994) The crypt cycle in mouse
small intestinal epithelium. J Cell Sci 107: 3271–3279.
45. Pinto D, Clevers H (2005) Wnt, stem cells and cancer in the intestine. Biology of
the cell 97: 185–196.
46. Potten CS, Loeffler M (1990) Stem cells: attributes, cycles, spirals, pitfalls and
uncertainties. Lessons for and from the crypt. Development 110: 1001–1020.
47. Auclair B, Benoit Y, Rivard N, Mishina Y, Perreault N (2007) Bone
morphogenetic protein signaling is essential for terminal differentiation of the
intestinal secretory cell lineage. Gastroenterology 133: 887–896.
48. Fevr T, Robine S, Louvard D, Huelsken J (2007) Wnt/beta-catenin is essential
for intestinal homeostasis and maintenance of intestinal stem cells. Mol Cell Biol
27: 7551–7559.
49. McGarvey MA, O’Kelly F, Ettarh RR (2007) Nimesulide inhibits crypt epithelial
cell proliferation at 6 hours in the small intestine in CD-1 mice. Dig Dis Sci 52:
2087–2094.
50. Biasco G, Cenacchi G, Nobili E, Pantaleo MA, Calabrese C, et al. (2004) Cell
proliferation and ultrastructural changes of the duodenal mucosa of patients
affected by familial adenomatous polyposis. Hum Pathol 35: 622–626.
51. Bransom CJ, Boxer ME, Palmer KR, Clark JC, Underwood JC, et al. (1981)
Mucosal cell proliferation in duodenal ulcer and duodenitis. Gut 22: 277–282.
52. Gorelick F, Sheahan D, DeLuca V (1979) In Vitro 3H-thymidine uptake in
duodenal mucosa from patients with duodenal ulcer or duodenitis. Gastroenterlogy 76: 1141.
53. Macdonald WC, Trier JS, Everett NB (1964) Cell Proliferation and Migration in
the Stomach, Duodenum, and Rectum of Man: Radioautographic Studies.
Gastroenterology 46: 405–417.
54. Potten CS (1998) Stem cells in gastrointestinal epithelium: numbers, characteristics and death. Philos Trans R Soc Lond B Biol Sci 353: 821–830.
55. Barker N, van Es JH, Kuipers J, Kujala P, van den Born M, et al. (2007)
Identification of stem cells in small intestine and colon by marker gene Lgr5.
Nature 449: 1003–1007.
56. Barker N, Clevers H (2007) Tracking down the stem cells of the intestine:
strategies to identify adult stem cells. Gastroenterology 133: 1755–1760.
57. Booth C, Booth D, Williamson S, Demchyshyn L, Potten CS (2004) Teduglutide
([Gly2]GLP-2) protects small intestinal stem cells from radiation damage. Cell
Prolif 37: 385–400.
58. Potten C (1977) Extreme sensitivity of some intestinal crypt cells to X and gama
irradiation. Nature 269: 518–521.
59. Potten C (2004) Radiation, the ideal cytotoxic agent for studying the cell biology
of tissues such as the small intestine. Radiat Res 161: 123–136.
60. Westerfield M (2007) The Zebrafish Book: a guide for the laboratory use of
zebrafish (Danio rerio). Oregon: University of Oregon Press.
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